Sequential explicit-implicit algorithm for computing discontinuous flows in porous media

M. A. Vegas-Landeau*, R. Propp, P. Colella, T. W. Patzek

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A novel numerical algorithm for computing incompressible, discontinuous, two-phase flows in two-dimensional, inhomogeneous, and isotropic porous media is presented. The algorithm uses Colella et al's. hybrid sequential explicit-implicit approach for both accuracy and speed of the calculations. The explicit part uses a high-order Godunov scheme with a modified Van Leer geometrical slope limiter, similar to those used in shock dynamics. The implicit part is a two-step solver: the first step is a Crank-Nicolson saturation solver and the second one is a Poisson solver for the phase pressure. Both use fast multilevel multigrid solvers with the number of operations of the order of θ[Nlog(N)], where N is the number of grid points. For an implicit simulator, the number of operations is θ(N3) per time step. Two numerically stiff reservoir engineering problems are presented to demonstrate the low numerical dispersion and second-order accuracy of our method.

Original languageEnglish (US)
Title of host publicationProduction Operations and Engineering/General
Pages871-884
Number of pages14
VolumePi
StatePublished - 1996
Externally publishedYes
EventProceedings of the 1996 Annual Technical Conference and Exhibition. Part Delta - Denver, CO, USA
Duration: Oct 6 1996Oct 9 1996

Other

OtherProceedings of the 1996 Annual Technical Conference and Exhibition. Part Delta
CityDenver, CO, USA
Period10/6/9610/9/96

ASJC Scopus subject areas

  • Geology
  • Geotechnical Engineering and Engineering Geology

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